When leaving London Hannay does this from a Station similar to Euston on a train made up of uniform Caledonian Railway Carriages bound for Inverness. The Loco shown is Apple Green suggesting it belonged to the North Eastern Railway. Inverness was accessible only by the Highland Railway. To get there from London Euston in the days of the story it would have been a trip via the LNWR to Carlisle which would have then been picked up by a Caledonian Railway loco to Aberdeen or Perth where a change would be required to the Highland Railway or the use of a Highland Railway Through Carriage on the train. The train would have been a hotchpotch of LNWR, CR and HR carriages.
The three cars which feature in the film (the grey Morris that Hannay and Victoria steal, the Germans' green Darracq and Hellory's blue Humber) were all registered in the mid 1920s and are models which would not have been available in 1914 when the action in the film takes place.
As the film is set before the start of the Great War in 1914, the featured biplane could not display red, white and blue RAF roundels as they were not introduced until December 1914: some months after the Great War had begun.
A one point Hannay is being chased by a bi-plane which fires at him with twin machine guns. These guns are firing through the propeller. This requires a synchronization gear (aka an interrupter gear).
The scene takes place in 1914 but the first synchronization gear was not installed on an aircraft until March 1915.
At the end of the movie Hannay is leaving London for the western front, but from St Pancras. He's at the wrong station. The line from there goes to the English Midlands, not the channel ports.
Captain Kell refers to his colleague as "Leftenant Commander". The Royal Navy at that time pronounced "Lieutenant" as "L'tenant".